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Continuous function and Hausdorff space

Shortcuts: Differences, Similarities, Jaccard Similarity Coefficient, References.

Difference between Continuous function and Hausdorff space

Continuous function vs. Hausdorff space

In mathematics, a continuous function is a function for which sufficiently small changes in the input result in arbitrarily small changes in the output. In topology and related branches of mathematics, a Hausdorff space, separated space or T2 space is a topological space in which distinct points have disjoint neighbourhoods.

Similarities between Continuous function and Hausdorff space

Continuous function and Hausdorff space have 19 things in common (in Unionpedia): Closed set, Compact space, Continuous function, Graph of a function, Kolmogorov space, Limit of a sequence, Mathematics, Metric space, Neighbourhood (mathematics), Net (mathematics), Open and closed maps, Open set, Quotient space (topology), Real number, Subspace topology, Surjective function, Topological space, Topology, Uniform space.

Closed set

In geometry, topology, and related branches of mathematics, a closed set is a set whose complement is an open set.

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Compact space

In mathematics, and more specifically in general topology, compactness is a property that generalizes the notion of a subset of Euclidean space being closed (that is, containing all its limit points) and bounded (that is, having all its points lie within some fixed distance of each other).

Compact space and Continuous function · Compact space and Hausdorff space · See more »

Continuous function

In mathematics, a continuous function is a function for which sufficiently small changes in the input result in arbitrarily small changes in the output.

Continuous function and Continuous function · Continuous function and Hausdorff space · See more »

Graph of a function

In mathematics, the graph of a function f is, formally, the set of all ordered pairs, and, in practice, the graphical representation of this set.

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Kolmogorov space

In topology and related branches of mathematics, a topological space X is a T0 space or Kolmogorov space (named after Andrey Kolmogorov) if for every pair of distinct points of X, at least one of them has a neighborhood not containing the other.

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Limit of a sequence

As the positive integer n becomes larger and larger, the value n\cdot \sin\bigg(\frac1\bigg) becomes arbitrarily close to 1.

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Mathematics

Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.

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Metric space

In mathematics, a metric space is a set for which distances between all members of the set are defined.

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Neighbourhood (mathematics)

In topology and related areas of mathematics, a neighbourhood (or neighborhood) is one of the basic concepts in a topological space.

Continuous function and Neighbourhood (mathematics) · Hausdorff space and Neighbourhood (mathematics) · See more »

Net (mathematics)

In mathematics, more specifically in general topology and related branches, a net or Moore–Smith sequence is a generalization of the notion of a sequence.

Continuous function and Net (mathematics) · Hausdorff space and Net (mathematics) · See more »

Open and closed maps

In topology, an open map is a function between two topological spaces which maps open sets to open sets.

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Open set

In topology, an open set is an abstract concept generalizing the idea of an open interval in the real line.

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Quotient space (topology)

In topology and related areas of mathematics, a quotient space (also called an identification space) is, intuitively speaking, the result of identifying or "gluing together" certain points of a given topological space.

Continuous function and Quotient space (topology) · Hausdorff space and Quotient space (topology) · See more »

Real number

In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.

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Subspace topology

In topology and related areas of mathematics, a subspace of a topological space X is a subset S of X which is equipped with a topology induced from that of X called the subspace topology (or the relative topology, or the induced topology, or the trace topology).

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Surjective function

In mathematics, a function f from a set X to a set Y is surjective (or onto), or a surjection, if for every element y in the codomain Y of f there is at least one element x in the domain X of f such that f(x).

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Topological space

In topology and related branches of mathematics, a topological space may be defined as a set of points, along with a set of neighbourhoods for each point, satisfying a set of axioms relating points and neighbourhoods.

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Topology

In mathematics, topology (from the Greek τόπος, place, and λόγος, study) is concerned with the properties of space that are preserved under continuous deformations, such as stretching, crumpling and bending, but not tearing or gluing.

Continuous function and Topology · Hausdorff space and Topology · See more »

Uniform space

In the mathematical field of topology, a uniform space is a set with a uniform structure.

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The list above answers the following questions

Continuous function and Hausdorff space Comparison

Continuous function has 150 relations, while Hausdorff space has 74. As they have in common 19, the Jaccard index is 8.48% = 19 / (150 + 74).

References

This article shows the relationship between Continuous function and Hausdorff space. To access each article from which the information was extracted, please visit:

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